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| {{Refimprove|date=December 2009}}
| | The title of the writer is Numbers. For a whilst I've been in South Dakota and my parents reside close by. Doing ceramics is what her family members and her enjoy. Managing individuals is his profession.<br><br>Visit my blog - [http://www.adosphere.com/poyocum std home test] |
| [[Image:Cartesian grid.svg|thumb|right|Example of a ''Cartesian grid''.]]
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| [[Image:Regular grid.svg|thumb|right|Example of a ''regular grid''.]]
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| [[Image:rectilinear grid.svg|thumb|right|Example of a ''rectilinear grid''.]]
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| [[Image:Curvilinear grid.svg|thumb|right|Example of a ''curvilinear grid''.]]
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| [[Image:Example curvilinear grid.svg|thumb|right|Another example of a ''curvilinear grid''.]]
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| A '''regular grid''' is a [[tessellation]] of '''''n'''''-dimensional [[Euclidean space]] by congruent [[parallelotope]]s (e.g. [[brick]]s).<ref>{{cite web|last=Uznanski, Dan.|title=Grid.|url=http://mathworld.wolfram.com/Grid.html|publisher=From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.|accessdate=25 March 2012}}</ref> Grids of this type appear on [[graph paper]] and may be used in [[finite element analysis]] as well as [[finite volume method]]s and [[finite difference method]]s. Since the derivatives of field variables can be conveniently expressed as finite differences,<ref name="Preface, P-1.1">{{cite book|last=J.F. Thompson, B. K . Soni & N.P. Weatherill|title=Handbook of Grid Generation|year=1998|publisher=CRC-Press|isbn=978-0-8493-2687-5|url=http://www.crcnetbase.com/isbn/9781420050349}}</ref> structured grids mainly appear in finite difference methods. [[Unstructured grid]]s offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods.
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| Each cell in the grid can be addressed by index (i, j) in two [[dimension]]s or (i, j, k) in three dimensions, and each [[vertex (geometry)|vertex]] has [[coordinate]]s <math>(i\cdot dx, j\cdot dy)</math> in 2D or <math>(i\cdot dx, j\cdot dy, k\cdot dz)</math> in 3D for some real numbers ''dx'', ''dy'', and ''dz'' representing the grid spacing.
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| ==Related grids==
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| A '''Cartesian grid''' is a special case where the elements are [[unit square]]s or [[unit cube]]s, and the vertices are [[integer point]]s.
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| A '''rectilinear grid''' is a tessellation by rectangles or [[parallelepiped]]s that are not, in general, all [[congruence (geometry)|congruent]] to each other. The cells may still be indexed by integers as above, but the mapping from indexes to vertex coordinates is less uniform than in a regular grid. An example of a rectilinear grid that is not regular appears on [[logarithmic scale]] [[graph paper]].
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| A '''curvilinear grid''' or '''structured grid''' is a grid with the same combinatorial structure as a regular grid, in which the cells are quadrilaterals or [[cuboid]]s rather than rectangles or rectangular parallelepipeds.
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| ==References==
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| {{Reflist}}
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| ==See also==
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| *[[Cartesian coordinate system]]
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| *[[Integer point]]
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| *[[Unstructured grid]]
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| {{DEFAULTSORT:Regular Grid}}
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| [[Category:Tessellation]]
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| [[Category:Lattice points]]
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| [[Category:Mesh generation]]
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| {{elementary-geometry-stub}}
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The title of the writer is Numbers. For a whilst I've been in South Dakota and my parents reside close by. Doing ceramics is what her family members and her enjoy. Managing individuals is his profession.
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